Is there a name for the way Maxima does algebra?

There is certainly room in the universe of symbolic computing for a purely
rule-based system.  However, it would very likely be unacceptably
inefficient for the run-of-the-mill applied math manipulation.

If you want to do operations in an algebraic system that is not one that
Maxima knows about, it is probably a good idea to avoid using + and * to
denote ANY operations in that system. Then the rules you supply are the only
simplifier, and you don't have to break anything in the existing one.  And
you won't slow down the existing simplifier at all.  If at some point you
want to do traditional + and *, either by some reduction or analogy or
something, you can substitute those operations in.  

Alternatively,

There are theorem proving systems and unification-based systems and specific
purpose group theory or number theory systems that are different from Maxima
in general outlook, and for some computations, closer to being right. 

Note that identities say A=B, but they don't tell you to convert A to B or B
to A.  And sometimes you run in both directions. E.g. trigexpand /
trigreduce  [not exactly opposites]  ;  demoivre /exponentialize . If you
impose some goal-driven search on transformations, you have a whole
different set of behaviors.



If you think everything can and should be done by rules, consider the very
important operation of collecting terms in a sum and sorting them.  You can
do this by rules, but probably shouldn't because it would be very slow.

The notion of adding rules to a general framework was present in a
rudimentary form in the original simplifier by Korsvold, in 1963, which is
still in Maxima, in part.  Tellsimp/ tellsimpafter, defrule, etc. were added
in 1968-71.  Reduce is another early system that had patterns and rules.
Mathematica places rules more centrally in its system, but warns people not
to mess with the simplification of built-in functions.  That's probably not
a bad idea for Maxima users as well.


RJF





> -----Original Message-----
> From: maxima-bounces at math.utexas.edu [mailto:maxima-
> bounces at math.utexas.edu] On Behalf Of Robert Dodier
> Sent: Monday, October 09, 2006 10:44 PM
> To: Chris Sangwin
> Cc: Maxima list
> Subject: Re: [Maxima] Is there a name for the way Maxima does algebra?
> 
..snip....